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Restriction and interpolation operators for digital images and their boundaries
Janosch Rieger, Kyria Wawryk
The aim of this paper is to provide a coherent framework for transforming boundary pairs of digital images from one resolution to another without knowledge of the full images. It i…
Towards optimal space-time discretization for reachable sets of nonlinear control systems
Janosch Rieger, Kyria Wawryk
Reachable sets of nonlinear control systems can in general only be approximated numerically, and these approximations are typically very expensive to compute. In this paper, we exp…
Generalized Gearhart-Koshy acceleration for the Kaczmarz method
Janosch Rieger
The Kaczmarz method is an iterative numerical method for solving large and sparse rectangular systems of linear equations. Gearhart, Koshy and Tam have developed an acceleration te…
Provably convergent implementations of the subdivision algorithm for the computation of invariant objects
Janosch Rieger
The subdivision algorithm by Dellnitz and Hohmann for the computation of invariant sets of dynamical systems decomposes the relevant region of the state space into boxes and analyz…
The Euler scheme for state constrained ordinary differential inclusions
Janosch Rieger
We propose and analyze a variation of the Euler scheme for state constrained ordinary differential inclusions under weak assumptions on the right-hand side and the state constraint…
Robust boundary tracking for reachable sets of nonlinear differential inclusions
Janosch Rieger
The Euler scheme is up to date the most important numerical method for ordinary differential inclusions, because the use of the available higher-order methods is prohibited by thei…
Semi-implicit Euler schemes for ordinary differential inclusions
Janosch Rieger
Two semi-implicit Euler schemes for differential inclusions are proposed and analyzed in depth. An error analysis shows that both semi-implicit schemes inherit favorable stability…